Juan Hernandez and his niece Diana Sanchez watch President Obama’s speech on state television in their apartment in Old Havana, a few blocks from theater where the U.S. president spoke. (Nick Miroff/The Washington Post)

In her apartment a few blocks from the theater where President Obama addressed the Cuban people Tuesday, Marta Limas and her family gathered around the television, opposite a faded shrine to Saint Lazarus, the healer.

The baby was crying. They turned up the volume.

“What a handsome man,” said Limas, 56, as Obama began, and quickly settled into a rhythm.

No one had spoken to the Cuban people with this kind of cadence in years. Limas and her family followed his words, rapt, as if listening to a sermon.

Obama called for change. “Yes, change!” the family repeated.

Obama talked the future. “The future!” they said.

Of all the U.S. president’s activities during his groundbreaking visit to Cuba, the speech was his best chance to speak directly to Cubans, both here on the island and abroad.

It wasn’t delivered in public, but it was broadcast in its entirety on Cuban state television, into the homes of many Cubans who, like Limas, talked about this visit as a turning point in their lives.

The family hushed and seemed to hold their breath when Obama’s words directly challenged their leaders, especially as the U.S. president called for democratic elections and urged President Raul Castro not to “fear the different voices of the Cuban people.” They admired his willingness to acknowledge the shortcomings and imperfections of the U.S. political system, and to have confidence in it anyway.

“I wish Fidel was there to hear this,” said Limas, of Cuba’s 89-year-old ailing former leader, who wasn’t in the audience at the theater with his 84-year-old brother, the president.

Limas’s husband, Juan Hernandez, 52, disagreed. “No, with Fidel everything would have stayed the same,” he said.

President Obama stopped at the José Martí Memorial in Havana as part of a wreath-laying ceremony. Obama also received a tour of the monument, which honors Martí, the Cuban poet and journalist. (Marcbassets and El Pais/Twitter)

Hernandez, a self-employed taxi driver, noted that he and Obama are nearly the same age. “I grew up indoctrinated in all this Cold War stuff,” he said. “I’m sick of it.”

Watching the family’s response to the U.S. president was somewhat like watching starry-eyed young Obama supporters at a speech during his 2008 campaign, before Americans grew accustomed to hearing him. Limas and her family were not.

That the U.S. president is African American also made an impression on the Afro-Cuban family.

“He’s a beautiful black man,” said Limas, when her husband stepped out of the room.

The family choked up with emotion at Obama’s words about the pain of family divisions and sense of loss among Cuban exiles. Limas’s first husband, the father of her two children, left for Miami in the 1980 Mariel boat lift and never looked back.

“May 4, 1980, at 6 a.m.,” Limas said. “That man walked right out this door.”

Duley Young, her daughter, 36, and the mother of the baby, grew up without him or his financial support. She earns a meager salary working for the city’s sanitation department. But she said she was sure that better days were ahead for Cuba after Obama’s visit.

“He’s turning everything around,” she said. “He said he isn’t trying to impose himself on the Cuban people.”

As the U.S. president finished, he was soon replaced on state television by pro-government commentators pointing out that voter turnout in U.S. presidential elections is barely 50 percent. They started picking apart other elements of Obama’s speech. Hernandez wouldn’t have it.

“Turn that off,” he said, waving at the television.

The room went quiet again, and the family lingered for a few minutes, talking about the speech. Obama’s appeal to young Cubans made a powerful impression on Limas, she said. Maybe it would persuade some of them to stay and not leave.

“I wish this had happened earlier,” she said. “Maybe there wouldn’t be so many deaths at sea.”